Using the <em>normal distribution and the central limit theorem</em>, it is found that there is a 0.1335 = 13.35% probability that 100 randomly selected students will have a mean SAT II Math score greater than 670.
<h3>Normal Probability Distribution</h3>
In a normal distribution with mean 
and standard deviation 
, the z-score of a measure X is given by:
- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
In this problem:
- The mean is of 660, hence
.
- The standard deviation is of 90, hence
.
- A sample of 100 is taken, hence
.
The probability that 100 randomly selected students will have a mean SAT II Math score greater than 670 is <u>1 subtracted by the p-value of Z when X = 670</u>, hence:
By the Central Limit Theorem
has a p-value of 0.8665.
1 - 0.8665 = 0.1335.
0.1335 = 13.35% probability that 100 randomly selected students will have a mean SAT II Math score greater than 670.
To learn more about the <em>normal distribution and the central limit theorem</em>, you can take a look at brainly.com/question/24663213
A table that shows the percentage of values ( or area percentage) to the left of a given z-score on a standard normal distribution
Answer:
Do you mind typing it your, your book is sorta blurry
Step-by-step explanation:
<u><em>Answer:</em></u>
ΔABP is congruent to ΔBAQ
ΔABP ≡ ΔBAQ
<u><em>Explanation:</em></u>
We are given two triangles; ΔABP and ΔABQ
<u>In these two triangles, we have:</u>
AB as a common side
∠ABP = ∠BAQ
AQ = BP
We can conclude that these two triangles are congruent by SAS (side-angle-side) postulate which states that:
"When two sides and the included angle between them in the first triangle are congruent to the corresponding two sides and the included angle between them in the second triangle, then the two triangles are congruent"
Note that when writing congruency statements, the order of the letters is critical as each angle/side in the first triangle must be congruent to its corresponding angle/side in the second triangle.
<u>Based on the above, the congruency statement would be:</u>
ΔABP is congruent to ΔBAQ
Hope this helps :)
Answer:
∠ FAB = 75°
Step-by-step explanation:
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ FAB is an external angle, thus
13x - 3 = 3x + 2 + 55 = 3x + 57 ( subtract 3x from both sides )
10x - 3 = 57 ( add 3 to both sides )
10x = 60 ( divide both sides by 10 )
x = 6
Thus
∠ FAB = 13x - 3 = 13(6) - 3 = 78 - 3 = 75°
